1. Field of the Invention
This invention generally relates to the carrier phase tracking of coded symbols, and, more specifically, to the use of reliability metrics of symbol estimates in the tracking process.
2. Related Art
During the decoding of coded symbols, particularly higher order symbols such as 8-PSK or QAM, there is a risk of cycle slippage of the symbol constellation. Cycle slippage is devastating to receiver performance. When it occurs, the symbol constellation rotates with respect to its true orientation such that another ostensibly valid constellation is interpreted at the receiver. This renders as useless all data decoded afterward. The problem is compounded with low operating Eb/No values, or with high phase noise in the demodulator oscillator or downconversion circuits. For example, at low Eb/No values, 8-PSK symbol error rates of 20-30% have been experienced. At such high error rates, decision-oriented phase tracking loops can experience great difficulty in following phase trends induced by instabilities of the demodulator oscillator and downconversion circuitry.
The invention provides a system for carrier phase tracking of coded symbols in which reliability metrics for the symbol estimates are used. Embodiments with a feed forward or feedback structure are possible.
In an embodiment with the feedforward structure, a received symbol is input to a tracking loop which includes a series combination of a symbol and reliability estimation engine, a tracking loop module, and a symbol derotator. The engine estimates the symbol, and also determines a reliability metric for the estimate.
The symbol estimate and reliability metric are input to the tracking loop module which determines a residual between the received symbol and its estimate. The residual may be a phase residual. The reliability metric for the estimate is used to weight the residual for the symbol. A derotation phase xcex8 is then determined responsive to the weighted residual. Optionally, one or more previous weighted residuals and one or more previous derotation phases are used in this process. A symbol derotator then derotates the symbol by the derotation phase xcex8. A delay element ensures proper synchronization of this process. The resulting phase adjusted symbol is then output by the derotator. The process may then repeat itself for subsequent symbols.
In one embodiment of the feedforward structure, the operation of this tracking loop may generally be described by the following expression:       θ    k    =                    ∑                  i          =          1                N            ⁢                        a          i                ·                  θ                      k            -            i                                +                  ∑                  i          =          0                          M          -          1                    ⁢                        b          i                ·                  R                      k            -            i                          ·                  z                      k            -            i                              
In this expression, xcex8k is the derotation phase at time k, xcex8kxe2x88x92i represents a previous value of the derotation phase at time kxe2x88x92i, ai is a coefficient applied to xcex8kxe2x88x92i, zkxe2x88x92i is a residual derived from rkxe2x88x92i, the (kxe2x88x92i)th received symbol and skxe2x88x92i, the estimate of that symbol, Rkxe2x88x92i is the reliability metric for the estimate of the (kxe2x88x92i)th symbol, bi is a coefficient applied to Rkxe2x88x92ixc2x7zkxe2x88x92i, and N and M are non-negative integers. In one embodiment, the residual zkxe2x88x92i is ekxe2x88x92i, the phase residual between rkxe2x88x92i and skxe2x88x92i. In another embodiment, the residual zkxe2x88x92i is the component of rkxe2x88x92i orthogonal to skxe2x88x92i.
In an embodiment with the feedback structure, a received symbol is input to a tracking loop which includes a series combination of a symbol derotator, a symbol and reliability estimation engine, and a tracking loop module. The received symbol is pre-rotated by the derotator using the best estimate of the derotation phase which is available at the time. The pre-rotated symbol is then input to the symbol and reliability estimation engine, which estimates the symbol, and also provides a reliability metric for the estimate. In the tracking loop module, a residual between the pre-rotated symbol and the estimate of that symbol is formed. The residual may be a phase residual. The residual is weighted by the reliability metric for the corresponding symbol estimate. A phase offset estimate is then determined responsive to the weighted residual. Optionally, one or more previous values of the weighted residuals, and one or more previous values of the phase offset estimate are used in this process. The phase offset estimate is then added to the value of the derotation phase (the one used to pre-rotate the symbol in the first place) to determine the next value of the derotation phase. Meanwhile, the pre-rotated symbol is output by the derotator. The process may then repeat itself for subsequent symbols.
In one embodiment of the feedback structure, the operation of the tracking loop may generally be described by the following two step process:             Δ      ⁢              xe2x80x83            ⁢              θ                  k          +          1                      =                            ∑                      i            =            0                                N            -            1                          ⁢                                            a              i                        ·            Δ                    ⁢                      xe2x80x83                    ⁢                      θ                          k              -              i                                          +                        ∑                      i            =            0                                M            -            1                          ⁢                              b            i                    ·                      R                          k              -              i                                ·                      z                          k              -              i                                                      θ              k        +        1              =                  θ        k            +              Δ        ⁢                  xe2x80x83                ⁢                  θ                      k            +            1                              
In this expression, xcex8k+1 is the derotation phase at time k+1, xcex8k+1 is the phase offset estimate at time k+1, xcex8kxe2x88x92i represents a previous value of the phase offset estimate at time kxe2x88x92i, a1 is a coefficient applied to xcex8kxe2x88x92i, zkxe2x88x92i is a residual derived from rkxe2x88x92i, the (kxe2x88x92i)th received symbol and skxe2x88x92i, the estimate of that symbol, Rkxe2x88x92i is the reliability metric for the estimate of the (kxe2x88x92i)th symbol, bi is a coefficient applied to Rkxe2x88x92ixc2x7zkxe2x88x92i, and N and M are non-negative integers. Note that the coefficients a1 and bi between this embodiment and the feedfoward embodiment.
In one embodiment, the residual zkxe2x88x92i is xkxe2x88x92i, the phase residual between tkxe2x88x92i, the pre-rotated value of the received symbol rkxe2x88x92i, and the estimate of that symbol, skxe2x88x92i. In another embodiment, the residual zkxe2x88x92i is the component of tkxe2x88x92i orthogonal to skxe2x88x92i.
In one example of the embodiment employing the feedback structure, the tracking loop employs a first order loop to determine the derotation phase xcex8. This first order loop can be expressed as follows:
xcex94xcex8k+1=Bxc2x7Rkxc2x7xk 
xcex8k+1=xcex8k+xcex94xcex8k+1 
where xcex8k+1, xcex94xcex8k+1,xcex8k, Rk, and xk are as defined previously, and B is a parameter which is proportional to the nominal loop bandwidth. The parameter B is typically less than 1 and a constant, and is configured to take account of noise. Typically, the more noise in the system, the smaller B is, and vice-versa. Note that the effective loop bandwidth in this example, Bxc2x7Rk, can vary from sample to sample, depending on the reliability Rk of the symbol estimate from which xk is computed.
In a second example of the embodiment employing the feedback structure, the tracking loop module employs a higher order loop to determine the derotation phase xcex8. This higher order loop may be expressed as follows:             Δ      ⁢              xe2x80x83            ⁢              θ                  k          +          1                      =          B      ·                        ∑                      i            =            0                                M            -            1                          ⁢                              R                          k              -              i                                ·                      x                          k              -              i                                                      θ              k        +        1              =                  θ        k            +              Δ        ⁢                  xe2x80x83                ⁢                  θ                      k            +            1                              
where the parameters xcex8k+1, xcex94xcex8k+, xcex8k, B, Rkxe2x88x92i, xkxe2x88x92i and M are as defined previously.
According to a third example of the embodiment employing the feedback structure, a technique is used in which a sinusoid of a function of the incremental phase residual at time k is used to update the derotation phase. In this example, the operation of the tracking loop may be represented by the following two step process:
xcex94xcex8k+1=Bxc2x7Rkxc2x7sin(Cxc2x7xk) 
xcex8k+xcex8k+xcex94xcex8k+1 
where the parameters xcex8k+, xcex94xcex8k+1, xcex8k, B, Rk, and xk, are as defined previously and C is a constant such that, when xk obtains its maximum value, sin(Cxc2x7xk)=0.
In a fourth example of the embodiment employing the feedback structure, the derotation phase at time k+1, xcex8k+1, is determined in accordance with the following formula:
xcex94xcex8k+1=xcex94xcex8k+Bxc2x7Rkxc2x7yk 
xcex8k+xcex8k+xcex94xcex8k+1 
In this example, the residual yk is the component of tk which is orthogonal to sk determined in accordance with the following formula:
yk=|tk|xc2x7sinxcfx86k 
where tk is the vector on the I-Q plane representing a pre-rotated received symbol rk, sk is the vector on the I-Q plane representing the estimate of rk, and xcfx86k is the phase difference between tk and sk.
In an example of the embodiment employing the feedfoward structure, the derotation phase at time k, xcex8k, is determined in accordance with the following formula:
xcex8k=xcex8kxe2x88x921+Bxc2x7Rkxc2x7ek 
where the parameters xcex8k, xcex8kxe2x88x921, B, Rk, and ek are as defined previously.
Other systems, methods, features and advantages of the invention will be or will become apparent to one with skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the invention, and be protected by the accompanying claims.